Author

zoo un park

packages used

Code 
library(tidyverse)
library(lubridate)
library(zoo)       
library(forecast)   
library(tseries)   
library(patchwork) 
library(here)
library(plotly)

Time series plot

Code 
uk = read.csv("../data/fx rate/UK_US.csv") 
uk <- uk %>% mutate(observation_date = as.Date(observation_date))%>%
  rename(UK_USD = DEXUSUK)%>%
  mutate(UK_USD = na.locf(UK_USD, na.rm = FALSE))

uk_plot <- ggplot(uk, aes(x = observation_date, y = UK_USD)) +
  geom_line(color = "blue") +
  labs(title = "GBP/USD Exchange Rate",
       x = "Date", y = "GBP(GBP per 1 USD)") +
  theme_minimal()

uk_plot

Code 
jp <- read_csv("../data/fx rate/JP_US.csv") %>%
  mutate(observation_date = as.Date(observation_date)) %>%
  rename(JP_USD = DEXJPUS,
         Date   = observation_date) %>%
  mutate( JP_USD = na.locf(JP_USD, na.rm = FALSE),
          USD_JP = 1 / JP_USD)  

jp_plot <- ggplot(jp, aes(x = Date, y = USD_JP)) +
  geom_line(color = "blue") +
  labs(title = "JPY/USD Exchange Rate ",
       x = "Date", y = "JPY(JPY per 1 USD)") +
  theme_minimal()

jp_plot

Code 
crude_oil <- read_csv(here("data/oil","oil_cleaned.csv")) %>%
  mutate(Date = as.Date(Date)) %>%
  arrange(Date) %>%
  mutate(across(-Date, ~ na.locf(.x, na.rm = FALSE)))

ggplot(crude_oil, aes(x = Date, y = WTI)) +
  geom_line(color = "darkgreen") +
  labs(title = "Crude Oil Prices", x = "Date", y = "Price") +
  theme_minimal()

Code 
sp500 <- read_csv(here("data/sp500","sp500_cleaned.csv")) %>%
  mutate(Date = as.Date(Date)) %>%
  arrange(Date) %>%
  mutate(across(-Date, ~ na.locf(.x, na.rm = FALSE)))

ggplot(sp500, aes(x = Date, y = Close)) +
  geom_line(color = "blue") +
  labs(title = "S&P 500 Index", x = "Date", y = "Level") +
  theme_minimal()

Code 
btc <- read_csv(here("data/btc","btc_cleaned.csv")) %>%
  mutate(Date = as.Date(Date)) %>%
  arrange(Date) %>%
  mutate(across(-Date, ~ na.locf(.x, na.rm = FALSE)))

ggplot(btc, aes(x = Date, y = Close)) +
  geom_line(color = "gold") +
  labs(title = "Bitcoin Price", x = "Date", y = "Price") +
  theme_minimal()

Code 
spread<- read_csv("../data/yield/merge_yield.csv")%>%
mutate(Date = as.Date(Date),
         Year = lubridate::year(Date)) %>%    
  arrange(Date)%>%
  mutate(across(ends_with("_spread"), ~ na.locf(.x, na.rm = FALSE))) %>%
  mutate(across(ends_with("_spread"), ~ na.locf(.x, fromLast = TRUE)))

jp_plot <- plot_ly(spread, x = ~Date, y = ~JP_Spread, type = 'scatter', mode = 'lines',
                   name = "Japan (10Y-2Y)") %>%
  layout(title = "Japan Yield Curve Spread (10Y-2Y)",
         xaxis = list(title = "Date"),
         yaxis = list(title = "Spread (%)"))
jp_plot
Code 
spread<- read_csv("../data/yield/merge_yield.csv")%>%
mutate(Date = as.Date(Date),
         Year = lubridate::year(Date)) %>%    
  arrange(Date)%>%
  mutate(across(ends_with("_spread"), ~ na.locf(.x, na.rm = FALSE))) %>%
  mutate(across(ends_with("_spread"), ~ na.locf(.x, fromLast = TRUE)))

eu_plot <- plot_ly(spread, x = ~Date, y = ~EU_Spread, type = 'scatter', mode = 'lines',
                   name = "EU (10Y-2Y)") %>%
  layout(title = "EU Yield Curve Spread (10Y-2Y)",
         xaxis = list(title = "Date"),
         yaxis = list(title = "Spread (%)"))
eu_plot
Code 
spread<- read_csv("../data/yield/merge_yield.csv")%>%
mutate(Date = as.Date(Date),
         Year = lubridate::year(Date)) %>%    
  arrange(Date)%>%
  mutate(across(ends_with("_spread"), ~ na.locf(.x, na.rm = FALSE))) %>%
  mutate(across(ends_with("_spread"), ~ na.locf(.x, fromLast = TRUE)))

uk_plot <- plot_ly(spread, x = ~Date, y = ~UK_Spread, type = 'scatter', mode = 'lines',
                   name = "UK (10Y-2Y)") %>%
  layout(title = "UK Yield Curve Spread (10Y-2Y)",
         xaxis = list(title = "Date"),
         yaxis = list(title = "Spread (%)"))
uk_plot
Code 
spread<- read_csv("../data/yield/merge_yield.csv")%>%
mutate(Date = as.Date(Date),
         Year = lubridate::year(Date)) %>%    
  arrange(Date)%>%
  mutate(across(ends_with("_spread"), ~ na.locf(.x, na.rm = FALSE))) %>%
  mutate(across(ends_with("_spread"), ~ na.locf(.x, fromLast = TRUE)))

eu_plot <- plot_ly(spread, x = ~Date, y = ~US_Spread, type = 'scatter', mode = 'lines',
                   name = "US (10Y-2Y)") %>%
  layout(title = "US Yield Curve Spread (10Y-2Y)",
         xaxis = list(title = "Date"),
         yaxis = list(title = "Spread (%)"))
eu_plot

Lag plots

Code 
jp_ts <- ts(jp$USD_JP, frequency = 252, start = c(year(min(jp$USD_JP))))
gglagplot(jp_ts, do.lines=FALSE) +
          xlab("Lags")+ylab("JYP/USD")

Code 
uk_ts <- ts(uk$UK_USD, frequency = 252, start = c(year(min(uk$UK_USD))))
gglagplot(jp_ts, do.lines=FALSE) +
          xlab("Lags")+ylab("UK/USD")

Code 
eu_ts <- ts(eu$EUR_USD, frequency = 252, start = c(year(min(eu$EUR_USD))))
gglagplot(jp_ts, do.lines=FALSE) +
          xlab("Lags")+ylab("EU/USD")

Code 
crude_oil_ts <- ts(crude_oil$WTI, frequency = 365, start = c(year(min(crude_oil$WTI))))
gglagplot(jp_ts, do.lines=FALSE) +
          xlab("Lags")+ylab("Crude oil price")

Code 
sp500_ts <- ts(sp500$Close, frequency = 252, start = c(year(min(sp500$Close))))
gglagplot(jp_ts, do.lines=FALSE) +
          xlab("Lags")+ylab("S&P500 index ")

Code 
btc_ts <- ts(btc$Close, frequency = 252, start = c(year(min(btc$Close))))
gglagplot(jp_ts, do.lines=FALSE) +
          xlab("Lags")+ylab("Bitcoin price")

Code 
jp_spread_ts <- ts(spread$JP_Spread, frequency = 252, start = c(year(min(spread$JP_Spread))))

gglagplot(jp_spread_ts, do.lines = FALSE) +
  labs(title = "Lag Plots of japan_spread",
       x = "Lags", y = "Japan spread %")

Code 
eu_spread_ts <- ts(spread$EU_Spread, frequency = 252, start = c(year(min(spread$EU_Spread))))

gglagplot(eu_spread_ts, do.lines = FALSE) +
  labs(title = "Lag Plots of euro_spread",
       x = "Lags", y = "Euro spread %")

Code 
uk_spread_ts <- ts(spread$UK_Spread, frequency = 252, start = c(year(min(spread$UK_Spread))))

gglagplot(uk_spread_ts, do.lines = FALSE) +
  labs(title = "Lag Plots of UK_spread",
       x = "Lags", y = "Uk spread %")

Code 
us_spread_ts <- ts(spread$US_Spread, frequency = 252, start = c(year(min(spread$US_Spread))))

gglagplot(us_spread_ts, do.lines = FALSE) +
  labs(title = "Lag Plots of US_spread",
       x = "Lags", y = "US spread %")

Decomposition

Code 
decompose_jp_ts <- decompose(jp_ts)
autoplot(decompose_jp_ts)

Code 
decompose_uk_ts <- decompose(uk_ts)
autoplot(decompose_uk_ts)

Code 
decompose_eu_ts <- decompose(eu_ts)
autoplot(decompose_eu_ts)

Code 
decompose_oil_ts <- decompose(crude_oil_ts)
autoplot(decompose_oil_ts)

Code 
decompose_sp500_ts <- decompose(sp500_ts)
autoplot(decompose_sp500_ts)

Code 
decompose_btc_ts <- decompose(btc_ts)
autoplot(decompose_btc_ts)

Code 
decompose_jp_spread_ts <- decompose(jp_spread_ts)
autoplot(decompose_jp_spread_ts)

Code 
decompose_eu_spread_ts <- decompose(eu_spread_ts)
autoplot(decompose_eu_spread_ts)

Code 
decompose_uk_spread_ts <- decompose(uk_spread_ts)
autoplot(decompose_uk_spread_ts)

Code 
decompose_us_spread_ts <- decompose(us_spread_ts)
autoplot(decompose_us_spread_ts)

ACF and PACF plots

Code 
ggAcf(jp_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of JPY currency rate") +
  theme_bw()

Code 
ggPacf(jp_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of JPY currency rate") +
  theme_bw()

Code 
#| echo: true
#| code-fold: true

ggAcf(uk_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of GBP currency rate") +
  theme_bw()

Code 
ggPacf(uk_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of GBP currency rate") +
  theme_bw()

Code 
#| echo: true
#| code-fold: true

ggAcf(eu_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of EUR currency rate") +
  theme_bw()

Code 
ggPacf(eu_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of EUR currency rate") +
  theme_bw()

Code 
#| echo: true
#| code-fold: true

ggAcf(crude_oil_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of Crude Oil Price") +
  theme_bw()

Code 
ggPacf(crude_oil_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of Crude Oil Price") +
  theme_bw()

Code 
#| echo: true
#| code-fold: true

ggAcf(sp500_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of S&P500 Index") +
  theme_bw()

Code 
ggPacf(sp500_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of S&P500 Index") +
  theme_bw()

Code 
ggAcf(btc_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of Bitcoin Price") +
  theme_bw()

Code 
ggPacf(btc_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of Bitcoin Price") +
  theme_bw()

Code 
ggAcf(jp_spread_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of Japan Spread Rate") +
  theme_bw()

Code 
ggPacf(jp_spread_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of Japan Spread Rate") +
  theme_bw()

Code 
ggAcf(eu_spread_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of Euro Spread Rate") +
  theme_bw()

Code 
ggPacf(eu_spread_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of Euro Spread Rate") +
  theme_bw()

Code 
ggAcf(us_spread_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of US Spread Rate") +
  theme_bw()

Code 
ggPacf(us_spread_ts) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of US Spread Rate") +
  theme_bw()

Augmented Dickey-Fuller Test


    Augmented Dickey-Fuller Test

data:  jp_ts
Dickey-Fuller = -1.3225, Lag order = 18, p-value = 0.8653
alternative hypothesis: stationary
Code 
adf.test(uk_ts)

    Augmented Dickey-Fuller Test

data:  uk_ts
Dickey-Fuller = -2.2011, Lag order = 18, p-value = 0.4932
alternative hypothesis: stationary
Code 
adf.test(eu_ts)

    Augmented Dickey-Fuller Test

data:  eu_ts
Dickey-Fuller = -2.1396, Lag order = 18, p-value = 0.5192
alternative hypothesis: stationary
Code 
adf.test(crude_oil_ts)

    Augmented Dickey-Fuller Test

data:  crude_oil_ts
Dickey-Fuller = -2.2326, Lag order = 13, p-value = 0.4799
alternative hypothesis: stationary
Code 
adf.test(sp500_ts)

    Augmented Dickey-Fuller Test

data:  sp500_ts
Dickey-Fuller = -1.4167, Lag order = 10, p-value = 0.8252
alternative hypothesis: stationary
Code 
adf.test(btc_ts)

    Augmented Dickey-Fuller Test

data:  btc_ts
Dickey-Fuller = -1.3955, Lag order = 15, p-value = 0.8343
alternative hypothesis: stationary
Code 
adf.test(jp_spread_ts)

    Augmented Dickey-Fuller Test

data:  jp_spread_ts
Dickey-Fuller = -2.2361, Lag order = 14, p-value = 0.4784
alternative hypothesis: stationary
Code 
adf.test(eu_spread_ts)

    Augmented Dickey-Fuller Test

data:  eu_spread_ts
Dickey-Fuller = -1.2324, Lag order = 14, p-value = 0.9013
alternative hypothesis: stationary
Code 
adf.test(uk_spread_ts)

    Augmented Dickey-Fuller Test

data:  uk_spread_ts
Dickey-Fuller = -1.1484, Lag order = 14, p-value = 0.9148
alternative hypothesis: stationary
Code 
adf.test(us_spread_ts)

    Augmented Dickey-Fuller Test

data:  us_spread_ts
Dickey-Fuller = -1.1226, Lag order = 14, p-value = 0.919
alternative hypothesis: stationary

Differencing

Code 
ggAcf(diff(log(jp_ts))) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of JPY currency rate") +
  theme_bw()

Code 
ggPacf(diff(log(jp_ts))) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of JPY currency rate") +
  theme_bw()

Code 
#| echo: true
#| code-fold: true

ggAcf(diff(log(uk_ts))) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of GBP currency rate") +
  theme_bw()

Code 
ggPacf(diff(log(uk_ts))) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of GBP currency rate") +
  theme_bw()

Code 
#| echo: true
#| code-fold: true

ggAcf(diff(log(eu_ts))) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of GBP currency rate") +
  theme_bw()

Code 
ggPacf(diff(log(eu_ts))) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of GBP currency rate") +
  theme_bw()

Code 
#| echo: true
#| code-fold: true

ggAcf(log(crude_oil_ts)) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of Crude Oil Price") +
  theme_bw()

Code 
ggPacf(log(crude_oil_ts)) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of Crude Oil Price") +
  theme_bw()

Code 
#| echo: true
#| code-fold: true

ggAcf(diff(log(sp500_ts))) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of S&P500 Index") +
  theme_bw()

Code 
ggPacf(diff(log(sp500_ts))) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of S&P500 Index") +
  theme_bw()

Code 
ggAcf(diff(log(btc_ts))) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of Bitcoin Price") +
  theme_bw()

Code 
ggPacf(diff(log(btc_ts))) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of Bitcoin Price") +
  theme_bw()

Code 
ggAcf(diff(jp_spread_ts)) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of Japan Spread Rate") +
  theme_bw()

Code 
ggPacf(diff(jp_spread_ts)) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of Japan Spread Rate") +
  theme_bw()

Code 
ggAcf(diff(eu_spread_ts)) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of Euro Spread Rate") +
  theme_bw()

Code 
ggPacf(diff(eu_spread_ts)) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of Euro Spread Rate") +
  theme_bw()

Code 
ggAcf(diff(us_spread_ts)) +
  geom_segment(aes(xend = lag, yend = 0), color="blue") +
  labs(title = "ACF of US Spread Rate") +
  theme_bw()

Code 
ggPacf(diff(uk_spread_ts)) +
  geom_segment(aes(xend = lag, yend = 0), color="red") +
  labs(title = "PACF of US Spread Rate") +
  theme_bw()

ADF test after differencing


    Augmented Dickey-Fuller Test

data:  diff(log(jp_ts))
Dickey-Fuller = -18.43, Lag order = 18, p-value = 0.01
alternative hypothesis: stationary
Code 
adf.test(diff(log(uk_ts)))

    Augmented Dickey-Fuller Test

data:  diff(log(uk_ts))
Dickey-Fuller = -18.859, Lag order = 18, p-value = 0.01
alternative hypothesis: stationary
Code 
adf.test(diff(log(eu_ts)))

    Augmented Dickey-Fuller Test

data:  diff(log(eu_ts))
Dickey-Fuller = -18.245, Lag order = 18, p-value = 0.01
alternative hypothesis: stationary
Code 
adf.test(diff(crude_oil_ts))

    Augmented Dickey-Fuller Test

data:  diff(crude_oil_ts)
Dickey-Fuller = -15.053, Lag order = 13, p-value = 0.01
alternative hypothesis: stationary
Code 
adf.test(diff(log(sp500_ts)))

    Augmented Dickey-Fuller Test

data:  diff(log(sp500_ts))
Dickey-Fuller = -11.132, Lag order = 10, p-value = 0.01
alternative hypothesis: stationary
Code 
adf.test(diff(log(btc_ts)))

    Augmented Dickey-Fuller Test

data:  diff(log(btc_ts))
Dickey-Fuller = -14.791, Lag order = 15, p-value = 0.01
alternative hypothesis: stationary
Code 
adf.test(diff(jp_spread_ts))

    Augmented Dickey-Fuller Test

data:  diff(jp_spread_ts)
Dickey-Fuller = -14.815, Lag order = 14, p-value = 0.01
alternative hypothesis: stationary
Code 
adf.test(diff(eu_spread_ts))

    Augmented Dickey-Fuller Test

data:  diff(eu_spread_ts)
Dickey-Fuller = -15.106, Lag order = 14, p-value = 0.01
alternative hypothesis: stationary
Code 
adf.test(diff(uk_spread_ts))

    Augmented Dickey-Fuller Test

data:  diff(uk_spread_ts)
Dickey-Fuller = -13.881, Lag order = 14, p-value = 0.01
alternative hypothesis: stationary

    Augmented Dickey-Fuller Test

data:  diff(us_spread_ts)
Dickey-Fuller = -13.978, Lag order = 14, p-value = 0.01
alternative hypothesis: stationary

Moving average

Code 
jp_df <- data.frame(Date = time(jp_ts), Value = as.numeric(jp_ts))
jp_df$MA20 <- rollmean(jp_df$Value, 20, fill = NA, align = "right")
jp_df$MA50 <- rollmean(jp_df$Value, 50, fill = NA, align = "right")
jp_df$MA100 <- rollmean(jp_df$Value, 100, fill = NA, align = "right")

plot_ly(jp_df, x = ~Date) %>%
  add_lines(y = ~Value, name = "JPY Rate", line = list(color = "black")) %>%
  add_lines(y = ~MA20, name = "MA20", line = list(color = "blue")) %>%
  add_lines(y = ~MA50, name = "MA50", line = list(color = "red")) %>%
  add_lines(y = ~MA100, name = "MA100", line = list(color = "green")) %>%
  layout(title = "JPY Currency Rate with Moving Averages",
         xaxis = list(title = "Date"),
         yaxis = list(title = "JPY rate"))
Code 
uk_df <- data.frame(Date = time(uk_ts), Value = as.numeric(uk_ts))
uk_df$MA20 <- rollmean(uk_df$Value, 20, fill = NA, align = "right")
uk_df$MA50 <- rollmean(uk_df$Value, 50, fill = NA, align = "right")
uk_df$MA100 <- rollmean(uk_df$Value, 100, fill = NA, align = "right")

plot_ly(uk_df, x = ~Date) %>%
  add_lines(y = ~Value, name = "GBP Rate", line = list(color = "black")) %>%
  add_lines(y = ~MA20, name = "MA20", line = list(color = "blue")) %>%
  add_lines(y = ~MA50, name = "MA50", line = list(color = "red")) %>%
  add_lines(y = ~MA100, name = "MA100", line = list(color = "green")) %>%
  layout(title = "GBP Currency Rate with Moving Averages",
         xaxis = list(title = "Date"),
         yaxis = list(title = "GBP rate"))
Code 
eu_df <- data.frame(Date = time(eu_ts), Value = as.numeric(eu_ts))
eu_df$MA20 <- rollmean(eu_df$Value, 20, fill = NA, align = "right")
eu_df$MA50 <- rollmean(eu_df$Value, 50, fill = NA, align = "right")
eu_df$MA100 <- rollmean(eu_df$Value, 100, fill = NA, align = "right")

plot_ly(eu_df, x = ~Date) %>%
  add_lines(y = ~Value, name = "EUR Rate", line = list(color = "black")) %>%
  add_lines(y = ~MA20, name = "MA20", line = list(color = "blue")) %>%
  add_lines(y = ~MA50, name = "MA50", line = list(color = "red")) %>%
  add_lines(y = ~MA100, name = "MA100", line = list(color = "green")) %>%
  layout(title = "EUR Currency Rate with Moving Averages",
         xaxis = list(title = "Date"),
         yaxis = list(title = "EUR rate"))
Code 
oil_df <- data.frame(Date = time(crude_oil_ts), Value = as.numeric(crude_oil_ts))
oil_df$MA20 <- rollmean(oil_df$Value, 20, fill = NA, align = "right")
oil_df$MA50 <- rollmean(oil_df$Value, 50, fill = NA, align = "right")
oil_df$MA100 <- rollmean(oil_df$Value, 100, fill = NA, align = "right")

plot_ly(oil_df, x = ~Date) %>%
  add_lines(y = ~Value, name = "Oil Price", line = list(color = "black")) %>%
  add_lines(y = ~MA20, name = "MA20", line = list(color = "blue")) %>%
  add_lines(y = ~MA50, name = "MA50", line = list(color = "red")) %>%
  add_lines(y = ~MA100, name = "MA100", line = list(color = "green")) %>%
  layout(title = "Crude Oil Price with Moving Averages",
         xaxis = list(title = "Date"),
         yaxis = list(title = "Oil Price"))
Code 
sp500_df <- data.frame(Date = time(sp500_ts), Value = as.numeric(sp500_ts))
sp500_df$MA20 <- rollmean(sp500_df$Value, 20, fill = NA, align = "right")
sp500_df$MA50 <- rollmean(sp500_df$Value, 50, fill = NA, align = "right")
sp500_df$MA100 <- rollmean(sp500_df$Value, 100, fill = NA, align = "right")

plot_ly(sp500_df, x = ~Date) %>%
  add_lines(y = ~Value, name = "S&P500", line = list(color = "black")) %>%
  add_lines(y = ~MA20, name = "MA20", line = list(color = "blue")) %>%
  add_lines(y = ~MA50, name = "MA50", line = list(color = "red")) %>%
  add_lines(y = ~MA100, name = "MA100", line = list(color = "green")) %>%
  layout(title = "S&P500 Index with Moving Averages",
         xaxis = list(title = "Date"),
         yaxis = list(title = "S&P500"))
Code 
btc_df <- data.frame(Date = time(btc_ts), Value = as.numeric(btc_ts))
btc_df$MA20 <- rollmean(btc_df$Value, 20, fill = NA, align = "right")
btc_df$MA50 <- rollmean(btc_df$Value, 50, fill = NA, align = "right")
btc_df$MA100 <- rollmean(btc_df$Value, 100, fill = NA, align = "right")

plot_ly(btc_df, x = ~Date) %>%
  add_lines(y = ~Value, name = "BTC Price", line = list(color = "black")) %>%
  add_lines(y = ~MA20, name = "MA20", line = list(color = "blue")) %>%
  add_lines(y = ~MA50, name = "MA50", line = list(color = "red")) %>%
  add_lines(y = ~MA100, name = "MA100", line = list(color = "green")) %>%
  layout(title = "Bitcoin Price with Moving Averages",
         xaxis = list(title = "Date"),
         yaxis = list(title = "BTC Price"))
Code 
jp_spread_df <- data.frame(Date = time(jp_spread_ts), Value = as.numeric(jp_spread_ts))
jp_spread_df$MA20 <- rollmean(jp_spread_df$Value, 20, fill = NA, align = "right")
jp_spread_df$MA50 <- rollmean(jp_spread_df$Value, 50, fill = NA, align = "right")
jp_spread_df$MA100 <- rollmean(jp_spread_df$Value, 100, fill = NA, align = "right")

plot_ly(jp_spread_df, x = ~Date) %>%
  add_lines(y = ~Value, name = "JP Spread", line = list(color = "black")) %>%
  add_lines(y = ~MA20, name = "MA20", line = list(color = "blue")) %>%
  add_lines(y = ~MA50, name = "MA50", line = list(color = "red")) %>%
  add_lines(y = ~MA100, name = "MA100", line = list(color = "green")) %>%
  layout(title = "Japan Spread with Moving Averages",
         xaxis = list(title = "Date"),
         yaxis = list(title = "Spread (bps)"))
Code 
eu_spread_df <- data.frame(Date = time(eu_spread_ts), Value = as.numeric(eu_spread_ts))
eu_spread_df$MA20 <- rollmean(eu_spread_df$Value, 20, fill = NA, align = "right")
eu_spread_df$MA50 <- rollmean(eu_spread_df$Value, 50, fill = NA, align = "right")
eu_spread_df$MA100 <- rollmean(eu_spread_df$Value, 100, fill = NA, align = "right")

plot_ly(eu_spread_df, x = ~Date) %>%
  add_lines(y = ~Value, name = "EU Spread", line = list(color = "black")) %>%
  add_lines(y = ~MA20, name = "MA20", line = list(color = "blue")) %>%
  add_lines(y = ~MA50, name = "MA50", line = list(color = "red")) %>%
  add_lines(y = ~MA100, name = "MA100", line = list(color = "green")) %>%
  layout(title = "Euro Spread with Moving Averages",
         xaxis = list(title = "Date"),
         yaxis = list(title = "Spread (bps)"))
Code 
uk_spread_df <- data.frame(Date = time(uk_spread_ts), Value = as.numeric(uk_spread_ts))
uk_spread_df$MA20 <- rollmean(uk_spread_df$Value, 20, fill = NA, align = "right")
uk_spread_df$MA50 <- rollmean(uk_spread_df$Value, 50, fill = NA, align = "right")
uk_spread_df$MA100 <- rollmean(uk_spread_df$Value, 100, fill = NA, align = "right")

plot_ly(uk_spread_df, x = ~Date) %>%
  add_lines(y = ~Value, name = "UK Spread", line = list(color = "black")) %>%
  add_lines(y = ~MA20, name = "MA20", line = list(color = "blue")) %>%
  add_lines(y = ~MA50, name = "MA50", line = list(color = "red")) %>%
  add_lines(y = ~MA100, name = "MA100", line = list(color = "green")) %>%
  layout(title = "UK Spread with Moving Averages",
         xaxis = list(title = "Date"),
         yaxis = list(title = "Spread (bps)"))
Code 
us_spread_df <- data.frame(Date = time(us_spread_ts), Value = as.numeric(us_spread_ts))
us_spread_df$MA20 <- rollmean(us_spread_df$Value, 20, fill = NA, align = "right")
us_spread_df$MA50 <- rollmean(us_spread_df$Value, 50, fill = NA, align = "right")
us_spread_df$MA100 <- rollmean(us_spread_df$Value, 100, fill = NA, align = "right")

plot_ly(us_spread_df, x = ~Date) %>%
  add_lines(y = ~Value, name = "US Spread", line = list(color = "black")) %>%
  add_lines(y = ~MA20, name = "MA20", line = list(color = "blue")) %>%
  add_lines(y = ~MA50, name = "MA50", line = list(color = "red")) %>%
  add_lines(y = ~MA100, name = "MA100", line = list(color = "green")) %>%
  layout(title = "US Spread with Moving Averages",
         xaxis = list(title = "Date"),
         yaxis = list(title = "Spread (bps)"))